Finite Group Databasebeta

← #13079293

Subgroups — #13079293

Order 1408.

374 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#542C211yesmaximal, characteristic, complemented
2#10623066C211yesmaximal, characteristic, complemented
3#10622701C211yesmaximal, characteristic, complemented
4#10622693C211yesmaximal, characteristic, complemented
5#10622671C211yesmaximal, characteristic, complemented
6#10622669C211yesmaximal, characteristic, complemented
7#10622662C211yesmaximal, characteristic, complemented
8#10622661C211yesmaximal, characteristic, complemented
9#10622652C211yesmaximal, characteristic, complemented
10#10622651C211yesmaximal, characteristic, complemented
11#10622639C211yesmaximal, characteristic, complemented
12C4×#4325C211yesmaximal, characteristic, complemented
13#10622627C211yesmaximal, characteristic, complemented
14C4×#4323C211yesmaximal, characteristic, complemented
15#10622610C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8C2211yescharacteristic
17C11×#126—21no—
18C11×#124—21no—
19C11×#124C2211yescharacteristic
20C11×#123—21no—
21C11×C22⋊Q8—21no—
22C11×C22⋊Q8C2211yescharacteristic
23C11×#121C2211yescharacteristic
24C4×Q8×C11C2211yescharacteristic
25C4×D4×C11C2211yescharacteristic
26C11×#117C2211yescharacteristic
27C2×#4325C2211yescharacteristic
28C2×#4325C2211yescharacteristic
29C2×#4323C2211yescharacteristic
30C2×#4323C2211yescharacteristic
31#66983C2211yescharacteristic
32#66983C2211yescharacteristic
33C2×#4318C2211yescharacteristic
34C22×C11⋊C8C2211yescharacteristic
35#66947—21no—
36#66947—21no—
37#66937—21no—
38#66937—21no—
39#66927C2211yescharacteristic
40C4×D44C2211yescharacteristic
41C4×D44C2211yescharacteristic
42#66923C2211yescharacteristic
43#66899C2211yescharacteristic
44#66899C2211yescharacteristic
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic
47#66873C2211yescharacteristic
48#66873C2211yescharacteristic
49#66873C2211yescharacteristic
50#66873C2211yescharacteristic
51#66872C2211yescharacteristic
52#66872C2211yescharacteristic
53#66871C2211yescharacteristic
54#66871C2211yescharacteristic
55#66867C2211yescharacteristic
56#66867C2211yescharacteristic
57C4×C11⋊C8C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11—21no—
62C2×D4×C11C2311yescharacteristic
63C22×C4×C11—21no—
64C22×C4×C11C2311yescharacteristic
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C2×D44—21no—
68C2×D44—21no—
69C2×D44C2311yescharacteristic
70C2×D44C2311yescharacteristic
71C2×C4×D11—21no—
72C2×C4×D11—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4—21no—
76C11×C4⋊C4D411yescharacteristic
77C11×C4⋊C4D411yescharacteristic
78C11×C4⋊C4C2311yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C11×C22⋊C4—21no—
81C11×C22⋊C4—21no—
82C11×C22⋊C4—21no—
83C11×C22⋊C4—21no—
84C11×C22⋊C4—21no—
85C11×C22⋊C4D411yescharacteristic
86C11×C22⋊C4D411yescharacteristic
87C42×C11—21no—
88C42×C11C2311yescharacteristic
89C42×C11C2311yescharacteristic
90#4325—22no—
91#4325—22no—
92#4323—22no—
93#4323—22no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98C4⋊Dic11C2311yescharacteristic
99C4⋊Dic11C2311yescharacteristic
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102#4318—22no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108#3179—111nomaximal, Sylow
109C23×C11—21no—
110C23×C11C2×D411yescharacteristic
111C22×D11—21no—
112C22×D11—21no—
113Q8×C11—21no—
114Q8×C11—21no—
115Q8×C11—81no—
116D4×C11—21no—
117D4×C11—21no—
118D4×C11—81no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—81no—
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2×D411yescharacteristic
128C2×C4×C11C2×D411yescharacteristic
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2411yescharacteristic
131C22⋊D11—81no—
132C22⋊D11—81no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135D44—21no—
136D44—21no—
137D44—21no—
138D44—21no—
139D44—81no—
140D44—81no—
141C4×D11—81no—
142C4×D11—81no—
143C11⋊C8—21no—
144C11⋊C8—21no—
145C11⋊C8#4112yes—
146C11⋊C8#4112yes—
147#542D1111yescharacteristic, complemented
148#540—111no—
149#501—111no—
150#496—111no—
151#488—111no—
152#486—111no—
153#469—111no—
154#468—111no—
155#466—111no—
156#465—111no—
157#442—111no—
158#440—111no—
159C4×SD16—111no—
160C4×D8—111no—
161#405—111no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11C22×D411yescharacteristic
169C2×D11—41no—
170C2×D11—41no—
171C2×D11—41no—
172C2×D11—41no—
173C2×D11—41no—
174C2×D11—41no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11C2×#4111yescharacteristic
184C4×C11C2×#4111yescharacteristic
185Dic11—41no—
186Dic11—41no—
187C2×SD16—111no—
188C2×SD16—111no—
189C2×D8—111no—
190C2×D8—111no—
191C2×M16—111no—
192C22×C8—111no—
193C4⋊Q8C2×D1111yescharacteristic
194#127—111no—
195#126—21no—
196#125—111no—
197#124—21no—
198#124C2×D1111yescharacteristic
199#123—21no—
200#123—221no—
201#123—221no—
202C22⋊Q8—21no—
203C22⋊Q8C2×D1111yescharacteristic
204#121—111no—
205#121—111no—
206#121—221no—
207#121—221no—
208#121C2×D1111yescharacteristic
209C4×Q8C2×D1111yescharacteristic
210C4×D4—111no—
211C4×D4—111no—
212C4×D4C2×D1111yescharacteristic
213#117C2×D1111yescharacteristic
214#107—111no—
215#107—111no—
216#106—111no—
217#106—111no—
218#103—111no—
219#103—111no—
220#102—111no—
221#102—111no—
222#102—111no—
223#102—111no—
224#102—111no—
225#102—111no—
226#97—111no—
227#97—111no—
228C4×C8—111no—
229C4×C8—111no—
230C2×C11—41no—
231C2×C11—81no—
232C2×C11#53211yescharacteristic
233C2×C11#57611yescharacteristic
234C2×C11#57711yescharacteristic
235D11—81no—
236D11—81no—
237C2×Q8—21no—
238C2×Q8C22×D1111yescharacteristic
239C2×D4—21no—
240C2×D4—111no—
241C2×D4—111no—
242C2×D4—221no—
243C2×D4—221no—
244C2×D4—221no—
245C2×D4—221no—
246C2×D4C22×D1111yescharacteristic
247C22×C4—21no—
248C22×C4—221no—
249C22×C4—221no—
250C22×C4C22×D1111yescharacteristic
251SD16—222no—
252SD16—222no—
253D8—222no—
254D8—222no—
255M16—222no—
256C2×C8—111no—
257C2×C8—111no—
258C2×C8—111no—
259C2×C8—111no—
260C2×C8—222no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—111no—
265C4⋊C4—111no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4C22⋊D1111yescharacteristic
269C4⋊C4C22⋊D1111yescharacteristic
270C4⋊C4C22×D1111yescharacteristic
271C4⋊C4C22×D1111yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—221no—
278C22⋊C4—221no—
279C22⋊C4—221no—
280C22⋊C4—221no—
281C22⋊C4C22⋊D1111yescharacteristic
282C22⋊C4C22⋊D1111yescharacteristic
283C42—21no—
284C42C22×D1111yescharacteristic
285C42C22×D1111yescharacteristic
286C11#317911yescharacteristic, complemented, Sylow
287C23—21no—
288C23—221no—
289C23—221no—
290C23C2×C22⋊D1111yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—81no—
294D4—21no—
295D4—21no—
296D4—81no—
297D4—221no—
298D4—221no—
299D4—221no—
300D4—221no—
301D4—881no—
302D4—881no—
303D4—881no—
304D4—881no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—221no—
312C2×C4—221no—
313C2×C4—881no—
314C2×C4—881no—
315C2×C4C2×C22⋊D1111yescharacteristic
316C2×C4C2×C22⋊D1111yescharacteristic
317C2×C4C2×C22⋊D1111yescharacteristic
318C2×C4C2×C22⋊D1111yescharacteristic
319C2×C4C2×C22⋊D1111yescharacteristic
320C2×C4C23×D1111yescharacteristic
321C8—112no—
322C8—112no—
323C8—221no—
324C8—221no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—441no—
332C22—441no—
333C22—441no—
334C22—441no—
335C22—441no—
336C22—441no—
337C22C22×C22⋊D1111yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—441no—
347C4—441no—
348C4#41×D1111yescharacteristic
349C4#41×D1111yescharacteristic
350C2—41no—
351C2—81no—
352C2—881no—
353C2—881no—
354C2#1062336311yescharacteristic
355C2#1062336611yescharacteristic
356C2#1062336811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#542C2
socleC22×C11C22×D4
hypercenter#542D11
hypocenterC11#3179
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C11×#542C2semidirect
2. #10623066C2semidirect
3. #10622701C2semidirect
4. #10622693C2semidirect
5. #10622671C2semidirect
6. #10622669C2semidirect
7. #10622662C2semidirect
8. #10622661C2semidirect
9. #10622652C2semidirect
10. #10622651C2semidirect
11. #10622639C2semidirect
12. C4×#4325C2semidirect
13. #10622627C2semidirect
14. C4×#4323C2semidirect
15. #10622610C2semidirect
147. #542D11semidirect
286. C11#3179semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C11×#5422
#106230662
#106227012
#106226932
#106226712
#106226692
#106226622
#106226612
#106226522
#106226512
#106226392
C4×#43252
#106226272
C4×#43232
#106226102
#317911